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Circulant matrices have been around for a long time and have been
extensively used in many scientific areas. This book studies the
properties of the eigenvalues for various types of circulant
matrices, such as the usual circulant, the reverse circulant, and
the k-circulant when the dimension of the matrices grow and the
entries are random. In particular, the behavior of the spectral
distribution, of the spectral radius and of the appropriate point
processes are developed systematically using the method of moments
and the various powerful normal approximation results. This
behavior varies according as the entries are independent, are from
a linear process, and are light- or heavy-tailed. Arup Bose
obtained his B.Stat., M.Stat. and Ph.D. degrees from the Indian
Statistical Institute. He has been on its faculty at the
Theoretical Statistics and Mathematics Unit, Kolkata, India since
1991. He is a Fellow of the Institute of Mathematical Statistics,
and of all three national science academies of India. He is a
recipient of the S.S. Bhatnagar Prize and the C.R. Rao Award. He is
the author of three books: Patterned Random Matrices, Large
Covariance and Autocovariance Matrices (with Monika Bhattacharjee)
and U-Statistics, M_m-Estimators and Resampling (with Snigdhansu
Chatterjee). Koushik Saha obtained a B.Sc. in Mathematics from
Ramakrishna Mission Vidyamandiara, Belur and an M.Sc. in
Mathematics from Indian Institute of Technology Bombay. He obtained
his Ph.D. degree from the Indian Statistical Institute under the
supervision of Arup Bose. His thesis on circulant matrices received
high praise from the reviewers. He has been on the faculty of the
Department of Mathematics, Indian Institute of Technology Bombay
since 2014.
Circulant matrices have been around for a long time and have been
extensively used in many scientific areas. This book studies the
properties of the eigenvalues for various types of circulant
matrices, such as the usual circulant, the reverse circulant, and
the k-circulant when the dimension of the matrices grow and the
entries are random. In particular, the behavior of the spectral
distribution, of the spectral radius and of the appropriate point
processes are developed systematically using the method of moments
and the various powerful normal approximation results. This
behavior varies according as the entries are independent, are from
a linear process, and are light- or heavy-tailed. Arup Bose
obtained his B.Stat., M.Stat. and Ph.D. degrees from the Indian
Statistical Institute. He has been on its faculty at the
Theoretical Statistics and Mathematics Unit, Kolkata, India since
1991. He is a Fellow of the Institute of Mathematical Statistics,
and of all three national science academies of India. He is a
recipient of the S.S. Bhatnagar Prize and the C.R. Rao Award. He is
the author of three books: Patterned Random Matrices, Large
Covariance and Autocovariance Matrices (with Monika Bhattacharjee)
and U-Statistics, M_m-Estimators and Resampling (with Snigdhansu
Chatterjee). Koushik Saha obtained a B.Sc. in Mathematics from
Ramakrishna Mission Vidyamandiara, Belur and an M.Sc. in
Mathematics from Indian Institute of Technology Bombay. He obtained
his Ph.D. degree from the Indian Statistical Institute under the
supervision of Arup Bose. His thesis on circulant matrices received
high praise from the reviewers. He has been on the faculty of the
Department of Mathematics, Indian Institute of Technology Bombay
since 2014.
a)Introduction of problem: The significant prognostic factors of
Wilms' tumor are- stage, age, anaplasia, size, capsular invasion,
etc. The role of DNA ploidy, proliferation markers is still not
proven. b)Abstract: Aims: This study was done to analyze the
histopathological spectrum of pediatric renal tumors and to study
the expression of Ki67, p53 and p27 in WT and correlate their
expression in epithelial and blastema components in different
stages of WT. Results: It was observed that the PI of Ki67 of
epithelial component was significantly higher than that of blastema
component in all stages. Proliferation index in stage II was
significantly higher than stage I. Statistical analysis could not
be done in stage III and stage IV due to small number of cases. p53
and p27 expression did not show any significant difference in
epithelial and blastema components and in between stages.
Conclusion: We found the differences of PI in different tissue
components of WT. The epithelial component having higher PI of
Ki67, which correlated well with the stage of advancement of the
disease. c) Target group: The book was written for the
pathologists, pediatric surgeons and urologists.
University libraries have to deal with the needs of researchers in
various disciplines preferably in science disciplines. The
requirements of research and researcher are ever changing and
dynamic in nature. To meet the ever growing needs of the science
scholars it is the responsibility of the university libraries to
provide right information to the right researchers in right form
and at the right time. Due to the advancement of the technology and
with the big hands of INFLIBNET, UGC Infonet E-consortium is come
into being to satisfy the needs of the scholars quickly and
rightly. Gradually, the e-journals come into being along with the
print journals. But there is a big question how far libraries are
able to meet the requirements of the science scholars even in the
21st century? How science scholars are friendly with the e-journals
concept? Etc. keeping these views in mind the present study is an
attempt to know the attitudes of the science research scholars
towards E-Journals in the Visva-Bharati, a Central University.
Considering the present library services regarding the usage of
E-Journal, the study has furnished some suggestions for the
betterment..
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